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A290741
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Orbit of word "2" under the 3-shift tag system over the alphabet {1,2} defined in the Comments.
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4
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2, 21222, 221221222, 2212221221222, 22212212221221222, 122122212212221221222, 1222122122212212222112, 21221222122122221122112, 212221221222211221121221222, 2212212222112211212212221221222, 22122221122112122122212212221221222, 222211221121221222122122212212221221222
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OFFSET
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1,1
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COMMENTS
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This tag system maps a word w over {1,2} to w', where if w begins with 1, w' is obtained by appending 2112 to w and deleting the first three letters, or if w begins with 2, w' is obtained by appending 1221222 to w and deleting the first three letters.
This is a 3-shift version of a 5-shift tag system studied in [De Mol, p. 307] (cf. A293945).
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LINKS
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MAPLE
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with(StringTools);
f1:=proc(w) local L, t2, t1, ws, w2;
t1:="2112"; t2:="1221222"; ws:=convert(w, string);
if ws[1]="1" then w2:=Join([ws, t1], ""); else w2:=Join([ws, t2], ""); fi;
L:=length(w2); if L <= 3 then return(-1); fi;
w2[4..L]; end;
# and apply f1 repeatedly to "2"
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PROG
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(Python)
from itertools import islice
def agen(w="2"):
while True:
yield int(w)
w += ("2112" if w[0] == "1" else "1221222")
w = w[3:]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Definition corrected by N. J. A. Sloane, Oct 23 2017 (this is not De Mol's 5-shift tag system, which is described in A293945).
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STATUS
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approved
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